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## Official Guide Explanation:Data Sufficiency #46

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 46
Page: 277
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Decimals >
Category 2: Arithmetic > Properties of Integers > Other
Category 3: Arithmetic > Fractions >

Explanation: Statement (1) is insufficient. If r is less than (1/3), in decimal terms it's less than 0.33. It could be 0.05, 0.15 or 0.25.

Statement (2) is sufficient. (1/10) = 0.1, so if r is less than (1/10), it must be 0.05. While a number can be negative, a single digit cannot be, so we don't have to worry about negative numbers less than (1/10). Choice (B) is correct.

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